Related papers: Holomorphic integer graded vertex superalgebras
We consider Lie superalgebras under constraints of Hamiltonian reduction, yielding finite $W$-superalgebras which provide candidates for quadratic spacetime superalgebras. These have an undeformed bosonic symmetry algebra (even generators)…
We discuss the classification of strongly regular vertex operator algebras (VOAs) with exactly three simple modules whose character vector satisfies a monic modular linear differential equation with irreducible monodromy. Our Main Theorem…
We describe the category of integrable sl(1|n)^ -modules with the positive central charge and show that the irreducible modules provide the full set of irreducible representations for the corresponding simple vertex algebra.
Some fine gradings on the exceptional Lie algebras $\mathfrak{e}_6$, $\mathfrak{e}_7$ and $\mathfrak{e}_8$ are described. This list tries to be exhaustive.
In this paper, we study Lie superalgebras of $2\times 2$ matrix-valued first-order differential operators on the complex line. We first completely classify all such superalgebras of finite dimension. Among the finite-dimensional…
In this paper, we give a generalization of results in \cite{PU07} and \cite{DPU10} by applying the tools of graded Lie algebras to quadratic Lie superalgebras. In this way, we obtain a numerical invariant of quadratic Lie superalgebras and…
The essential feature of a root-graded Lie algebra L is the existence of a split semisimple subalgebra g with respect to which L is an integrable module with weights in a possibly non-reduced root system S of the same rank as the root…
We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.
We provide a complete classification of unitary subalgebras of even rank-one lattice vertex operator algebras. As a consequence of the correspondence between vertex operator algebras and conformal nets, we also obtain a complete…
A general notion of a quasi-finite algebra is introduced as an algebra graded by the set of all integers equipped with topologies on the homogeneous subspaces satisfying certain properties. An analogue of the regular bimodule is introduced…
Superderivations for the eight families of finite or infinite dimensional graded Lie superalgebras of Cartan-type over a field of characteristic $p>3$ are completely determined by a uniform approach: The infinite dimensional case is reduced…
The classification of graded non-alternating Hamiltonian Lie algebras over perfect field of characteristic 2 is obtained. It is shown that the filtered deformations of such algebras correspond to non-alternating Hamiltonian forms with…
In this work the classification of filiform Leibniz superalgebras of nilindex $n+m,$ where $n$ and $m$ ($m \ne 0$) are dimensions of even and odd parts, respectively, is obtained.
A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading (including the trivial grading). We show that a…
In this paper, Lie conformal superalgebras of rank (2 + 1) are completely classified (up to isomorphism) and their automorphism groups are determined. Furthermore, we give the classification of the finite irreducible conformal modules over…
The arXiv:2105.09738 claims several stuffs. In particular, we recall the following two. (1) Vector fields and differential forms become a Lie superalgebra structure for each manifold. (2) For an n-dimensional Euclidean space, vector fields…
We describe the classification of orthogonal arrays OA$(2048,14,2,7)$, or, equivalently, completely regular $\{14;2\}$-codes in the $14$-cube ($30848$ equivalence classes). In particular, we find that there is exactly one…
The invariants of all complex solvable rigid Lie algebras up to dimension eight are computed. Moreover we show, for rank one solvable algebras, some criteria to deduce to non-existence of non-trivial invariants or the existence of…
We classify all simple bounded highest weight modules of a basic classical Lie superalgebra $\mathfrak g$. In particular, our classification leads to the classification of the simple weight modules with finite weight multiplicities over all…
In this paper, we continue the study on toroidal vertex algebras initiated in \cite{LTW}, to study concrete toroidal vertex algebras associated to toroidal Lie algebra $L_{r}(\hat{\frak{g}})=\hat{\frak{g}}\otimes L_r$, where…